1. Field of the Invention
This invention relates to the field of tiles and tilings. The field includes the familiar floor and kitchen-counter top tiles and tilings and their like, but also extends to the sometimes more abstract areas of art, design, and mathematics.
2. Some Definitions
I have adapted a few of the notions and definitions of the mathematics of patterns and tilings as follows. A tile is a two-dimensional closed shape which fits together edge-to-edge with other similar or different two-dimensional shapes, as do jig-saw puzzle pieces or bricks, to cover a flat surface of indefinite extent. Such a covering is called a tiling if it has no gap between tiles nor any overlap of one tile on another. Adding thickness to a two-dimensional tile will make it a three-dimensional object which is also called a tile. A tile is said to tile the plane if indefinitely large numbers of duplicates of the tile can fit together without gap or lap to form a tiling. The term the plane refers to the flat and indefinitely extensive plane of Euclidian geometry.
A figurative tile is one whose shape is the recognizable outline, or figure, of a person or an animal. A figurative tiling is a tiling composed of such figurative tiles. A variably assemblable tile is a tile shaped so that duplicates of it will fit together with one another in a variety of different ways, allowing a plurality of different tilings to be made.
A line or figure is point symmetric if a half-turn makes the line or figure coincide with itself. Line symmetry, or reflective symmetry, is the specifically 2-dimensional version of the more inclusive term bilateral symmetry, in which one half of a line or figure is the mirror image of the other half.
An amphographic line is a line which is used in more than one location in forming the outline of a figurative tile. Each side of an amphographic line draws, or gives positive form to, a different part of the outline of the figurative tile, so that, for example, a curve in the line which at one point is a bulge on the figure's outline, at another point is a depression. In devising a figurative tile, amphographic lines are used to connect the vertices of an ancestral straight-line geometric figure of a sort chosen so that the completed figurative outline, when replicated, and perhaps reflected to form mirror images, can tile the plane. An ancestral geometric figure can be thought of as an underlying invisible geometric determiner of vertex locations.
The tile shapes comprised in this invention are called Ozbirds tiles or are referred to simply as tiles, or Ozbirds.
3. Prior Art
Other than in my own work, there is no prior example of single-shape figurative tiles which are variably assemblable into tilings of the plane.
4. Objects and Advantages
It is an object of the invention to provide a puzzle piece, duplicates of which are capable of fitting together with one-another in a variety of ways, and with which various tiling tasks of puzzle-like sorts can be accomplished. It is also an object of the invention to provide a decorative figurative tile shape which can form varied tilings for use on any surface where they are desired such as paper, plastic, woven fabric, architectural surfaces and pavings, or can be used in various ways in conjunction with a computer or a computer program, or can be used to give amusing shape to manipulable food items such as cookies.